That was a very thorough answer for a 'big fat shrugsville'. :)
I have always thought the concept of multiple universes was a possibility. It could not be empirically proven, but neither could the existence of God or ghosts or military intelligence, and yet some people believed in them.
However, this does not mean they do not exist. Paul Steinhardt argued that no experiment can rule out a theory if the theory provides for all possible outcomes.
The philosopher Chrysippus in the Third Century B.C. suggested that the world eternally expired and regenerated, effectively suggesting the existence of multiple universes across time. That is perpetuated with the Brane multiverse proposal, that we are one of many universes each existing on a membrane, floating around and occasionally interacting and very rarely colliding and creating a Big Bang, a cyclic reboot for those universes who would then start again.
I do not think this is our situation. There are too many variables and we would have to play with Strings and have extra spacial dimensions, and it is just more complicated than we need to be. Expanding from that idea, though, and yes, taking into account the metaphysical aspect to this situation, we are probably experiencing a quantum multiverse, created when a diversion in events occurs, like the MWI of quantum mechanics.
Essentially, this incursion from another universe near us, or dimension, whatever word you please, and the use of the Time Stone created the splintering of our universe, the Prime one, into this one and possibly created others, too. How or why the Doctor 'popped' into it would be interesting to pursue.
Applying a consciousness to this fractured universe an unusual route. We do not tend to think of something as massive and complicated as a universe being an entity which can make decisions and act upon them, like pulling certain people into this new 'mistake' to 'fix' things as it might perceive them. This seems like a stretch to me, even with magic in the mix.